Animating grouped meshes with shape keys
To make object change its shape while animating complex movings like trees it's better to use rigging with Armature modifier than the shape keys.

Shape keys are generally used as an additional geometry changer working together with armature, i.e. they aren't armature substitution. They aren't as flexible as rigging because they can be added to one object and thus edit only that object; also one has to define the final form of the object initially in order key to work.

To animate a tree moving it's a good idea to rig that tree. Create a skeleton for it, use any method to skin a tree and create some poses for the tree leaves and / or trunk.







Note: When creating tree with Sapling: Add Tree addon it's possible to add an armature for the tree: